The study of Evolution and understanding the history of life on Earth, has attracted scientists’ attention since the dawn of modern science. Phylogenetics, the reconstruction of this history, has expanded beyond its traditional role in evolutionary studies and with the advent of next generation sequencing is increasingly integrated into modern biological areas such as preventive medicine, epidemiology, and human migration. Maximum Likelihood (ML) is considered as the most accurate phylogenetic method. Our lab has developed expertise in analytical solutions to ML phylogenetic reconstruction. The novelty of our approach is the representation of the ML problem as a constraint optimization problem and using algebraic geometry tools for obtaining the solution. The work [2] appeared in RECOMB, the world’s most important bioinformatics conference and have since sparked a wave of interest in this approach, in particular among mathematicians from UC Berkeley where I later took on a position

as a postdoctoral research fellow. The work relies on the Hadamard Conjugation [8, 7], a very elegant mathematical tool in phylogenetics. As part of this project, together with Mike Hendy, the inventor of the “Hadamard”, we provided a combinatorial proof for the tool for the family of Kimura models of DNA evolution [9]. It is said in Joe Felsenstein’s book [5], the “bible” of phylogenetics, on the hadamard conjugation, “This is one of the nicest applications of mathematics to phylogenetics so far”!  We are honored to be part, although tiny, of this line of research.

Later on, we extended this framework to analyze phylogenetic networks.

Analytical ML is still our method of choice and a prevailing approach in almost every project we undertake in genomics.